Polynomial division

I just cant remember how to do this!!! Ive been to several sites suggesting synthetic division and other guides on polynomial division but i cant get it into my head and its driving me wild. :surprised

(8x-8)/(x^2+3x+2)

synthetic division doesn't work here because the denominator is larger than the numerator..... right?

Heres my work ive done w/ that P/Q method:

(x^2+3x+2) = (x+2)(x+1)

therefore use the format:

8x-8 = A/(x+2) + B(x+1)
and solve for A and B

This is where im stuck. I went further and solved A = 16 and B = -8 and pluged it in to get

16/(x+2) - 8/(x+1) but this doesnt equal (8x-8) / (x^2+3x+2) !!!!!!!

Im stuck!!! can someone please enlighten me? Thanks a ton!

OR: If anyone has a good helpful website that they know of that shows polynomial division when the Denominator is larger than the numerator id appreciate it. I can only find the sites where the numerator is larger than the denominator